Godina izdanja: Ostalo
ISBN: Ostalo
Jezik: Engleski
Oblast: Matematika
Autor: Strani

Kazimierz Kuratowski - Introduction to Set Theory and Topology
Pergamon Press, New York / Panstwowe Wydawnictwo Naukowe, Warszawa 1961
283 str.
tvrdi povez
stanje: dobro, potpis na predlistu.

Translated from the Revised Polish Edition by Leo F. Boron.

International Series of Monographs on Pure and Applied Mathematics Volume 13.

`Kazimierz Kuratowski`s main work was in the area of topology and set theory. He used the notion of a limit point to give closure axioms to define a topological space. He wrote an important textbook Set Theory and Topology for beginners. An English edition was published in 1961 with the Foreword to this edition written in Warsaw in September 1960. In this Foreword Kuratowski writes: `The ideas and methods of set theory and topology permeate modern mathematics. It is no wonder then that the elements of these two mathematical disciplines are now an indispensable part of basic mathematical training. Concepts such as the union and intersection of sets, countability, closed set, metric space, and homeomorphic mapping are now classical notions in the whole framework of mathematics. The purpose of the present volume is to give an accessible presentation of the fundamental concepts of set theory and topology; special emphasis being placed on presenting the material from the viewpoint of its applicability to analysis, geometry, and other branches of mathematics such as probability theory and algebra. Consequently, results important for set theory and topology but not having close connection with other branches of mathematics, are given a minor role or are omitted entirely. Such topics are, for instance, axiomatic investigations, the theory of alephs, and the theory of curves`

Introduction to Set Theory and Topology describes the fundamental concepts of set theory and topology as well as its applicability to analysis, geometry, and other branches of mathematics, including algebra and probability theory. Concepts such as inverse limit, lattice, ideal, filter, commutative diagram, quotient-spaces, completely regular spaces, quasicomponents, and cartesian products of topological spaces are considered.
This volume consists of 22 chapters organized into two sections and begins with an introduction to set theory, with emphasis on the propositional calculus and its application to propositions each having one of two logical values, 0 and 1. Operations on sets which are analogous to arithmetic operations are also discussed. The chapters that follow focus on the mapping concept, the power of a set, operations on cardinal numbers, order relations, and well ordering. The section on topology explores metric and topological spaces, continuous mappings, cartesian products, and other spaces such as spaces with a countable base, complete spaces, compact spaces, and connected spaces. The concept of dimension, simplexes and their properties, and cuttings of the plane are also analyzed.
This book is intended for students and teachers of mathematics.

FOREWORD TO THE ENGLISH EDITION, Pages 11-12
INTRODUCTION TO PART I, Pages 17-22
CHAPTER I - PROPOSITIONAL CALCULUS, Pages 23-26
CHAPTER II - ALGEBRA OF SETS. FINITE OPERATIONS, Pages 27-38
CHAPTER III - PROPOSITIONAL FUNCTIONS. CARTESIAN PRODUCTS, Pages 39-49
CHAPTER IV - THE MAPPING CONCEPT. INFINITE OPERATIONS. FAMILIES OF SETS, Pages 50-64
CHAPTER V - THE CONCEPT OF THE POWER OF A SET. COUNTABLE SETS, Pages 65-72
CHAPTER VI - OPERATIONS ON CARDINAL NUMBERS. THE NUMBERS a AND c, Pages 73-84
CHAPTER VII - ORDER RELATIONS, Pages 85-90
CHAPTER VIII - WELL ORDERING, Pages 91-106
INTRODUCTION TO PART II, Pages 109-114
CHAPTER IX - METRIC SPACES. EUCLIDEAN SPACES, Pages 115-122
CHAPTER X - TOPOLOGICAL SPACES, Pages 123-136
CHAPTER XI - BASIC TOPOLOGICAL CONCEPTS, Pages 137-144
CHAPTER XII - CONTINUOUS MAPPINGS, Pages 145-164
CHAPTER XIII - CARTESIAN PRODUCTS, Pages 165-175
CHAPTER XIV - SPACES WITH A COUNTABLE BASE, Pages 176-184
CHAPTER XV - COMPLETE SPACES, Pages 185-189
CHAPTER XVI - COMPACT SPACES, Pages 190-222
CHAPTER XVII - CONNECTED SPACES, Pages 223-239
CHAPTER XVIII - LOCALLY CONNECTED SPACES, Pages 240-253
CHAPTER XIX - THE CONCEPT OF DIMENSION, Pages 254-258
CHAPTER XX - SIMPLEXES AND THEIR PROPERTIES, Pages 259-272
CHAPTER XXI - CUTTINGS OF THE PLANE, Pages 273-290
LIST OF IMPORTANT SYMBOLS, Pages 343-344


Nonfiction, Mathematics